Lemma 21.53.3. Let $\mathcal{C}$ be a site with final object $X$. Let $\Lambda $ be a ring. Let $K, L$ be objects of $D(\Lambda )$ with $K$ perfect. Let $\varphi : \underline{K} \to \underline{L}$ be map in $D(\mathcal{C}, \Lambda )$. There exists a covering $\{ U_ i \to X\} $ such that $\varphi |_{U_ i}$ is equal to $\underline{\alpha _ i}$ for some map $\alpha _ i : K \to L$ in $D(\Lambda )$.

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